The Wisdom Of Trees (Leonardo Da Vinci Knew It)

Leonardo DaVinci noted that when trees branch, smaller branches have a precise, mathematical relationship to the branch they sprang from.

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Originally published on January 9, 2012 1:15 pm

Hurricanes topple plenty of trees, but when you think about it, the more amazing thing is that many trees can stand up to these 100-mile-per-hour winds.

Now a French scientist has come up with an explanation for the resilience of trees. And astonishingly, the answer was first described by Leonardo da Vinci 500 years ago.

Leonardo noticed that when trees branch, smaller branches have a precise, mathematical relationship to the branch from which they sprang. Many people have verified Leonardo's rule, as it's known, but no one had a good explanation for it.

French physicist Christophe Eloy wasn't particularly interested in trees, but he does specialize in understanding how air flows around objects — objects like airplane wings and such. So he decided to see whether he could solve the mystery of the branching trees.

"I just did it because it was a nice problem, but I think there are some implications for real-life applications," Eloy says.

Leonardo's rule is fairly simple, but stating it mathematically is a bit, well, complicated. Eloy did his best:

"When a mother branch branches in two daughter branches, the diameters are such that the surface areas of the two daughter branches, when they sum up, is equal to the area of the mother branch."

Translation: The surface areas of the two daughter branches add up to the surface area of the mother branch.

'A Very Nice Challenge'

While Eloy was on a break from his day job as an assistant professor of physics at the University of Provence, he started playing around with some calculations, and he came across something rather amazing. From an engineering point of view, if you wanted to design a tree that was best able to withstand high winds, it would branch according to Leonardo's rule.

Apparently, trees have figured out the sophisticated engineering principles all on their own.

Of course, engineers have known for a long time that they have to think about wind when they're building things.

"The most famous example for a man-made structure that was built with wind load considerations in mind is the Eiffel Tower," says Pedro Reis, a professor of engineering at the Massachusetts Institute of Technology. Reis says the Eiffel Tower's shape was based not just on aesthetics but on those design principles trees know all about. He says Eloy's work could be useful for designing branch structures like those in complex antennas.

But that's a bonus. Reis says he understands exactly what Eloy means when he says he didn't tackle the conundrum of Leonardo's rule because he expected it to have practical implications.

"When you see something like that that hasn't been explored fully, it's a very nice challenge for a scientist. So I'm not surprised that Christophe took that onboard and did such an elegant study," he says.

Hurricanes knock over a lot of trees, but when you think about it, the more amazing thing is that many trees withstand 100-mile-an-hour winds. Now a French scientist has come up with an explanation. And astonishingly the answer was first described by Leonardo da Vinci centuries ago. NPR's Joe Palca has our report.

JOE PALCA, BYLINE: Five hundred years ago, Leonardo da Vinci noticed that when trees branch, smaller branches have a precise, mathematical relationship to the branch they sprung from. Many people have verified Leonardo's Rule, as it's known, but no one had a good explanation for it.

French physicist Christophe Eloy wasn't particularly interested in trees, but he specializes in understanding how air flows around objects - objects like airplane wings and such. So he decided to see if he could solve the mystery of the branching trees.

CHRISTOPHE ELOY: I just did it because it was a nice problem. But I think there are some implications for real-life applications.

PALCA: Leonardo's Rule is fairly simple, but stating it mathematically is a bit, well, complicated. Eloy did his best.

ELOY: When a mother branch branches in two daughter branches, the diameters are such that the surface area of the two daughter branches, when they sum up, it is equal to the area of the mother branch.

PALCA: Did you get that? Will repetition help? The surface areas of the two daughter branches add up to the surface area of the mother branch.

Anyway, while Eloy was on a break from his day job as an assistant professor of physics at the University of Provence, he started playing around with some calculations and he came across something rather amazing. From an engineering point of view, if you wanted to design a tree that was best able to withstand high winds it would branch according to Leonardo's rule.

Apparently, trees have figured out this sophisticated engineering principle all on their own. Of course, engineers have known for a long time that they have to think about wind when they're building things. Pedro Reis is an engineer at the Massachusetts Institute of Technology.

PEDRO REIS: The most famous example for a man-made structure that was built with wind load considerations in mind is the Eiffel Tower.

PALCA: Reis says the Eiffel Tower's shape was not just based on aesthetics, but on those design principles trees know all about. He says Eloy's work could be useful for designing other branch structures, like complex antennas. But that's a bonus. Reis says he understands exactly what Christophe Eloy means when he says he didn't tackle the conundrum of Leonardo's Rule because he expected it to have practical implications.

REIS: When you see something historical like that hasn't really been explored fully, it's a very nice challenge for a scientist. So I'm not surprised that Christophe took that on board and did such an elegant study.

PALCA: If you want to know more about the details of what Eloy did, you can find them in the journal Physical Review Letters.

Joe Palca, NPR News, Washington.

INSKEEP: Of course, scientists never tire of asking the question why. And their answers are sometimes amazing to the simplest things. Pedro Reis of MIT has explored his own problem - why the pages of a book or magazine make a certain noise, a regular clapping sound when left on a beach blanket on a windy day. You can see a video explanation of that phenomenon by visiting our website, NPR.org.